Page 114 - Mechanical Engineers' Handbook (Volume 4)

5 The Laws of Thermodynamics for Open Systems 103

Figure 2 The energy minimum principle, or the entropy maximum principle.

˙ m ˙ m M
in out t
}
mass transfer mass change
Subscripts in and out refer to summation over all the inlet and outlet ports, respectively,
while M stands for the instantaneous mass inventory of the control volume.
The first law of thermodynamics is more general than the statement encountered earlier
for closed systems, because this time we must account for the flow of energy associated
with the ˙m streams:

˙ mh V 2 gZ V 2 gZ Q W E
˙
˙
˙ mh
in 2 out 2 i i t
energy transfer energy change
On the left-hand side we have the energy interactions: heat, work, and the energy transfer
associated with mass flow across the control surface. The specific enthalpy h, fluid velocity
V, and height Z are evaluated right at the boundary. On the right-hand side, E is the instan-
taneous system energy integrated over the control volume.
The second law of thermodynamics for an open system assumes the form
˙ ms ˙ ms Q i S
˙
in out i T i t
}
entropy transfer entropy change
The specific entropy s is representative of the thermodynamic state of each stream right at
the system boundary. The entropy generation rate is defined by